RUDN University mathematicians have developed a model for calculating the density of 5G stations needed to achieve the required network parameters. The results are published in *Computer Communications*.

Network slicing (NS) is one of the key technologies that the new 5G communication standard relies on. Several virtual networks, or layers, are deployed on the same physical infrastructure (the same base stations). Each layer is allocated to a separate group of users, devices, or applications. To slice the network, one need the NR (New Radio) technology, which operates on millimetre waves. Most of the research in this area is aimed at creating an infrastructure of NR stations that would provide network slicing in each specific case. RUDN University mathematicians have developed a first general theoretical approach that helps to calculate the density of NR base stations needed to slice the network with the specified parameters of the quality of service.

"The concept of network slicing will drastically simplify the market entrance for mobile virtual network operators as well as provisioning of differentiated quality to network services. This functionality is a major paradigm shift in the cellular world enabling multi-layer network structures similar to that of the modern Internet and allowing resource sharing with logical isolation among multiple tenants and/or services in multi-domain context", said Ekaterina Lisovskaya, PhD, junior Researcher at the Research Center for Applied Probability & Stochastic Analysis at RUDN University.

When constructing the algorithm, the RUDN mathematicians used a model city. NR base stations were distributed with some density. The stations had three antennas, each of which covered 120 degrees. Users of devices with 5G cellular communication network operating in the millimetre frequency range (30-100 GHz) were randomly distributed around the city. They moved and could block each other's line-of-sight with the base station. Each antenna had an effective range, where the connection doesn't break even if the line-of-sight is blocked. The RUDN University mathematicians constructed the dependence of the network characteristics on the density of the station location.

To check the accuracy of the constructed model, mathematicians used a computer simulation. The results of theoretical and experimental calculations agreed. The model shows, for example, how the density of the stations affects the regime of network splitting from full isolation to full mixing. The first one assumes that each layer has its own frequency range of a fixed width. In the second regime, the frequencies of the layers are mixed with each other. The second option is more difficult from a technical point of view, but it increases the efficiency of using physical network resources. RUDN University mathematicians have studied these regimes as two boundary versions of the network implementation -- in real life, some intermediate implementation is usually required. It turned out that the difference in the density of stations between these bounds is small -- one station per 10,000 square meters.

"Our numerical evaluation campaign reveals that the full isolation and full mixing systems' operational regime changes rather abruptly with respect to the density of NR BSs. However, the system parameters may drastically affect the required density. Practically, it implies that at the initial market penetration phase, the full isolation strategy can be utilized without compromising the network performance. However, at mature deployment phases, more sophisticated schemes may reduce the capital expenditures of network operators" said Ekaterina Lisovskaya, PhD, junior Researcher at the Research Center for Applied Probability & Stochastic Analysis at RUDN University.

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Computer Communications